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THE WEST COAST OF BRITAIN: STATISTICAL SELF‐SIMILARITY VS. CHARACTERISTIC SCALES IN THE LANDSCAPE
Author(s) -
ANDRLE ROBERT
Publication year - 1996
Publication title -
earth surface processes and landforms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.294
H-Index - 127
eISSN - 1096-9837
pISSN - 0197-9337
DOI - 10.1002/(sici)1096-9837(199610)21:10<955::aid-esp639>3.0.co;2-y
Subject(s) - fractal , scale (ratio) , range (aeronautics) , linearity , west coast , similarity (geometry) , curvature , fractal dimension , self similarity , geology , fractal analysis , maxima , mathematics , physical geography , geography , statistics , geometry , cartography , oceanography , physics , history , computer science , mathematical analysis , materials science , artificial intelligence , image (mathematics) , composite material , quantum mechanics , art history , performance art
Abstract Mandelbrot (Science, 1967, 156, 636–638) used the west coast of Britain as an example of a naturally occurring statistically self‐similar fractal. Evidence from this study indicates that the west coast of Britain is not statistically self‐similar over the range of scale of measurement, and that complexity reaches maxima at characteristic scales related to identifiable features on the coastline. A fractal analysis is conducted using the divider method, and although the resulting log–log plot of measured length against steplength appears linear, statistical tests for linearity strongly suggest that the coastline is not statistically self‐similar. An angle measure technique (AMT) developed by the author to examine changes in line complexity with scale, shows that within the range of scale of measurement there are two peaks in complexity for the west coast of Britain, suggesting that two processes acting at different scales have influenced coastal development. The AMT is also used to identify differences in complexity between northern and southern sections of the coastline. Additionally, high r 2 values associated with regressions of log L ( G ) against log G are shown to be insufficient evidence of statistical self‐similarity, and apparently linear segments (fractal elements) often found in Richardson plots may contain systematic curvature revealed only by more rigorous tests for non‐linearity.